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J. Chem. Eng. Data 2007, 52, 817-832

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Solubility of CO2 in Aqueous Solutions of KCl and in Aqueous Solutions of K2CO3 A Ä lvaro Pe´ rez-Salado Kamps, Eckehard Meyer, Bernd Rumpf, and Gerd Maurer* Applied Thermodynamics, University of Kaiserslautern, P.O. Box 30 49, D-67653 Kaiserslautern, Germany

A high-pressure view-cell technique based on the synthetic method was used to determine the total pressure above aqueous solutions of two single salts (potassium chloride and potassium carbonate) and carbon dioxide. In the series of measurements with potassium chloride, the molality of the salt amounted to about (2 and 4) mol‚(kg of water)-1, the temperature ranged from about (313 to 433) K, and the molality of carbon dioxide ranged up to about 1 mol‚(kg of water)-1, corresponding to a maximum pressure of about 9.4 MPa. In the series of measurements with potassium carbonate, the stoichiometric molality of that salt amounted to about (0.43 and 1.7) mol‚(kg of water)-1 (stoichiometric mass fraction of the salt of about 0.056 and 0.19, respectively), the temperature ranged from about (313 to 393) K, and the ratio of the stoichiometric molalities of carbon dioxide to potassium carbonate ranged from about 0.7 to 3.6, corresponding to pressures from about (0.27 to 9.2) MPa. The vapor-liquid equilibrium of the systems (CO2 + KCl + H2O) and (CO2 + K2CO3 + H2O) (the latter allowing for the precipitation of KHCO3 that is important in connection with the “Hot Potassium Carbonate (Benfield) Process” and its modifications by activating additives) is described by means of a thermodynamic model based on Pitzer’s molality scale based equation for the Gibbs excess energy of the aqueous phase. Model parameters are determined from the new carbon dioxide solubility data as well as from an extensive database adopted from the literature.

Introduction The so-called “Hot Potassium Carbonate (Benfield) Process” uses aqueous potassium carbonate solutions for removal of sour gases carbon dioxide and hydrogen sulfide from ammonia synthesis gas, natural gas, crude hydrogen, etc. by “chemical” absorption.1-4 The gas absorption takes place at temperatures well above ambient (around 343 K and higher) and at elevated pressures (up to about 2 MPa or more), whereas gas desorption (that is, solvent regeneration in the stripper) occurs at elevated temperatures (up to about 403 K) and low pressures (in particular at low partial pressures of the sour gases). The absorption of carbon dioxide in aqueous solutions of potassium carbonate is hampered by slow chemical reaction kinetics. In particular, the formation of bicarbonate is kinetically hindered.5 However, relatively high temperature in the absorber highly enhances the absorption rate of carbon dioxide. In addition, high temperature greatly increases the solubility of potassium bicarbonate, therefore allowing operation with highly concentrated solutions.6 Typically, the stoichiometric mass fraction of potassium carbonate in water ranges from about 0.2 to 0.3 {stoichiometric potassium carbonate molalities from about (1.8 to 3.1) mol‚(kg of water)-1},6 but it may reach up to 0.4 {4.8 mol‚(kg of water)-1}.3 Process modifications intend to further accelerate the absorption of carbon dioxide by activating additives. Furthermore, to impede corrosion, appropriate inhibitors are added. For example, the so-called “Catacarb Process” uses aqueous solutions of potassium carbonate and an undisclosed additive that incorporates a corrosion-inhibiting component.6 In most cases, the absorption of carbon dioxide is promoted by the addition of secondary and primary amines,7,8 for example, diethanolamine (DEA), which is the original Benfield activator,6 * Corresponding author. Tel.: +49 631 205 2410. Fax: +49 631 205 3835. E-mail: [email protected].

piperazine,9,10 or even ammonia. These substances quickly and reversibly chemically react with carbon dioxide to form not only carbamate species but also bicarbonate through so-called “reversion” of the carbamate species. Deviation from equilibrium provides the driving force in a kinetically controlled process. Therefore, to properly design and optimize the separation equipment, equilibrium properties (mainly the chemical reaction equilibrium, the vapor-liquid equilibrium (VLE) as well as information on the energy to vaporize/condense the mixtures) need to be known. In particular, modeling the phase equilibrium for the simultaneous solubility of carbon dioxide and hydrogen sulfide in aqueous solutions of potassium carbonate plus additives requires a reliable and extensive experimental database on the solubility of the single gases in aqueous solutions of potassium carbonate as well as in aqueous solutions of the single additives. The present work focuses on one of the interesting subsystems, namely, (CO2 + K2CO3 + H2O). A thermodynamic model for describing the VLE of the system (CO2 + K2CO3 + H2O), which also accounts for the precipitation of potassium bicarbonate (KHCO3), is developed. The model is based on Pitzer’s molality scale-based equation for the Gibbs excess energy of the aqueous phase. Model parameters describing interactions between potassium and carbonate ions are based on experimental data for the vapor pressure above aqueous solutions of potassium carbonate as compiled from the literature by Aseyev.11 These parameters are valid for temperatures from about 298 K up to at least 473 K and for stoichiometric mass fractions of potassium carbonate in water up to at least 0.5 {stoichiometric molalities of 7.2 mol‚ (kg of water)-1}. Model parameters mainly describing interactions between potassium and bicarbonate ions but also between potassium, bicarbonate, and carbonate ions in the low gas loading (low pressure) region (that is, at stoichiometric molar ratios of carbon dioxide to potassium carbonate below one) are

10.1021/je060430q CCC: $37.00 © 2007 American Chemical Society Published on Web 03/03/2007

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determined from an extensive equilibrium database. That database covers experimental results by Tosh et al.3 for the solubility of carbon dioxide in aqueous solutions of potassium carbonate [at temperatures from about 343 K up to 413 K, stoichiometric mass fractions of potassium carbonate from 0.2 to 0.4 {stoichiometric molalities from about (1.8 to 4.8) mol‚ (kg of water)-1}, stoichiometric molar ratios of carbon dioxide to potassium carbonate from 0.1 to about 0.88, and partial pressures of carbon dioxide up to about 0.92 MPa]. In addition, the database includes experimental data for the solubility of the salt potassium bicarbonate in water and in aqueous solutions of carbon dioxide and potassium carbonate (for temperatures from 273 K to 415 K).1,12,13 Furthermore, in the present work a high-pressure view-cell technique based on the synthetic method is used to determine the solubility pressure of carbon dioxide above aqueous solutions of potassium chloride. The molality of the salt amounts to about (2 and 4) mol‚(kg of water)-1, the temperature ranges from about (313 to 433) K, and the molality of carbon dioxide ranges up to about 1 mol‚(kg of water)-1, corresponding to a maximum pressure of about 9.4 MPa. These new carbon dioxide solubility data in aqueous solutions of potassium chloride are used to determine model parameters describing interactions between carbon dioxide and potassium ions in aqueous solutions. Those parameters are thereby valid for temperatures from (313 to 433) K, so they cover the relevant temperature range for the Hot Potassium Carbonate Process. By including these parameters in the model for the VLE of the system (CO2 + K2CO3 + H2O), the model allows us to make predictions of the carbon dioxide solubility pressure in the high gas loading region, where it is difficult to gain experimental information. To evaluate the model predictions, a few new experimental results for the solubility of carbon dioxide in aqueous solutions of potassium carbonate were taken in the high gas loading regionsagain by means of the high-pressure view-cell technique mentioned above. In these experimental series, the stoichiometric molality of potassium carbonate amounted to about (0.43 and 1.7) mol‚(kg of water)-1 (stoichiometric mass fraction of the salt of about 0.056 and 0.19, respectively), the temperature ranged from about (313 to 393) K, and the ratio of the stoichiometric molalities of carbon dioxide to potassium carbonate ranged from about 0.7 to 3.6, corresponding to pressures from about (0.27 to 9.2) MPa. The model is able to reliably predict these new experimental results in the high gas loading region. Finally, the few experimental data for the solubility of carbon dioxide in aqueous solutions of either potassium chloride or potassium carbonate found in the open literature are compared with predicted results from the new model.

Experimental Section Apparatus and Method. The apparatus used to measure the solubility of carbon dioxide in the given solvent (an aqueous solution of either potassium chloride or potassium carbonate) is based on the synthetic method. The equipment is particularly suited for elevated pressures from about 0.2 MPa up to 20 MPa and more. Its central part is an equilibrium cell with a known volume (approximately 30 cm3). Prior to the series of gas solubility measurements, the cell volume is accurately determined at a fixed temperature by means of a high-precision displacement pump (Ruska Instrument Corporation, Houston, TX, type 2241). Proper corrections are applied to account for the small amount of thermal expansion. At any temperature, the volume of the cell is known to within ( 0.1 %. Details on the gas solubility measuring technique can be found in previous publications.14-17

Figure 1. Estimated speciation (a, K+; b, OH-; c, CO32-; d, HCO3-; e, / j KOH ) CO2) in aqueous solutions of (CO2 + KOH) at T ) 353.15 K, m 4 mol‚kg-1. (Comments on this figure are given in the text and in Appendix 1.)

In an experiment, the pressure which is required to dissolve, at a constant and preset temperature, a precisely known amount of gas in a precisely known amount of solvent is determined. When the mass of carbon dioxide, which is filled into the cell is small {here smaller than about 1.3 g, which was the case for all CO2 solubility measurements in (KCl + H2O)}, it is determined volumetrically from the known volume of the cell and readings for temperature and pressure by applying an appropriate equation of state.18 When the mass of the gas filled into the cell is large {here larger than about 1.3 g and up to about 6 g, which was the case for all CO2 solubility measurements in (K2CO3 + H2O)}, it is determined gravimetrically by weighing a condenser from which the cell is charged, before and after the charging process on a high-precision balance. Gravimetric uncertainties amount to ( 0.012 g. The mass of solvent filled into the cell (approximately 30 g) is calculated from the volume displacement in a calibrated spindle press and the solvent density with a relative uncertainty of about 0.15 %. The density of the solvent is known from separate measurements with a vibrating-tube densimeter (Anton Paar GmbH, Graz, Austria). Two calibrated platinum resistance thermometers were used to determine the temperature. The uncertainty of the temperature measurement is better than ( 0.1 K. When carbon dioxide was volumetrically filled into the cell, the pressure was measured with two pressure transducers suitable for pressures ranging up to (2.5 and 4) MPa, respectively. The solubility pressure itself was measured with two other pressure transducers suitable for pressures up to (6 and 10) MPa, respectively. Commercially available electronic pressure transducers (WIKA GmbH, Klingenberg, Germany) were used. The maximum systematic uncertainty in the solubility pressure measurement results from the uncertainty of the pressure transducers (0.1 % of the transducer’s full scale) and an additional contribution of about ( 0.01 MPa caused by a small temperature drift in the isolated tubes filled with solvent, which connect the cell with the pressure transducers. The temperature drift contribution was determined in test runs. All pressure transducers were calibrated against a high-precision pressure gauge (Desgranges & Huot, Aubervilliers, France) before and after each series of measurements. Preliminary Comments. Figure 1 shows a predicted speciation in an aqueous solution of potassium hydroxide and carbon / / dioxide, where m j KOH denote the “stoichiometric” and m j CO 2 molality of these two components {that is, the amount of

Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007 819

substance (the number of moles) of a component per kilogram of water} and where m/i denotes the “true” molality of all solute species i {that is, the “true” amount of substance (the “true” number of moles) of solute species i per “true” kilogram of water} present in appreciable amounts, namely, potassium (K+), hydroxide (OH-), carbonate (CO32-), bicarbonate (HCO3-), and molecular carbon dioxide (CO2). The speciation was calculated by adopting the chemical reaction equilibrium constants (for the hydrolysis of water and for the formation of carbonate and bicarbonate) from the literature19-21 and by estimating the activity coefficients of all species from Pitzer’s modification of the Debye-Hu¨ckel term alone.22,23 / / There are three regions. In region I (m j CO /m j KOH < 1/2), 2 carbon dioxide almost completely reacts with potassium hydroxide to form potassium carbonate and water: CO2(aq) + 2KOH(aq) f K2CO3(aq) + H2O(l)

(I)

In this region, the liquid mixture can be regarded as an aqueous solution of potassium carbonate and potassium hydroxide, where carbon dioxide has been practically completely chemically absorbed. Hence, in region I, the partial pressure of carbon dioxide above the solution is almost zero. / / / / In regions II and III (1/2 < m j CO /m j KOH < 1 and m j CO /m j KOH 2 2 > 1, respectively), the liquid mixture can be regarded as an aqueous solution of potassium carbonate, potassium bicarbonate, and carbon dioxide: CO2(aq) + K2CO3(aq) + H2O(l) h 2KHCO3(aq)

(II)

In region II, most carbon dioxide is chemically absorbed, but some carbon dioxide is dissolved physically, which results in a small but appreciable partial pressure of the gas above the solution. In region III, a considerable amount of carbon dioxide is physically dissolved, which results in a remarkable increase of the total pressure with an increase in the amount of the dissolved gas. Consequently, in connection with the design of absorption/desorption processes of carbon dioxide in such potassium containing solutions, only regions II and III are of importance. In this context, it is therefore reasonable to express the composition of such solutions by the stoichiometric molalities of carbon dioxide (the absorbed acid gas) and potassium j K2CO3). Region II carbonate (as the basic electrolyte) (m j CO2, m (0 < m j CO2/m j K2CO3 < 1) may be denominated as the low gas j K2CO3 > loading (low pressure) region, and region III (m j CO2/m 1) may be denominated as the high gas loading (high pressure) region. The equations to convert the stoichiometric molalities / / (m j KOH and m j CO ) to (m j K2CO3 and m j CO2) are given in Appen2 dix 1. Materials and Sample Pretreatment. Deionized water was degassed by vacuum distillation. Carbon dioxide (mole fraction g 99.995 %) was purchased from Messer-Griesheim (Ludwigshafen, Germany). It was used without further purification. Potassium chloride (p.a., mass fraction g 99.5 %) and potassium hydroxide hydrate (p.a., mass fraction KOH g 85 %, mass fraction K2CO3 < 1 %, rest is mainly water) were purchased from Merck GmbH (Darmstadt, Germany). They were degassed and dried under vacuum for several hours. The aqueous solutions of the strong electrolytes (either KCl or KOH) were prepared in a storage tank. The gravimetric uncertainty of the stoichiometric molality of KCl was smaller than about ( 0.02 %. The stoichiometric molality of KOH was determined titrimetrically with a relative uncertainty smaller than about ( 1.6 %. The resulting relative uncertainty of the stoichiometric molality of K2CO3 in the aqueous solution is smaller than ( 1.6 %. For the CO2 solubility measurements in

Table 1. Experimental Results for the Total Pressure above Aqueous Solutions of Potassium Chloride and Carbon Dioxide T K 315.8 313.25 316.15 313.25 313.25 313.35 313.6 313.6 333.1 333.15 333.15 333.15 333.15 333.15 353.0 353.05 353.0 353.05 353.05 353.05 353.05 373.05 373.05 373.05 373.1 373.1 373.1 373.1 393.1 393.1 393.1 393.1 393.1 393.1 393.05 413.05 413.05 413.1 413.1 413.1 413.1 413.05 413.05 433.05 433.05 433.05 433.1

m j KCl

m j CO2

mol‚kg-1 mol‚kg-1 1.994

1.994

1.942

1.942

1.942

1.942

1.942

0.1235 0.1390 0.2941 0.3052 0.4340 0.6210 0.8213 1.0197 0.2831 0.2837 0.4201 0.5491 0.6709 0.8215 0.0374 0.1771 0.1765 0.3111 0.4295 0.5637 0.6787 0.0427 0.1456 0.1468 0.2612 0.3749 0.5398 0.5795 0.0641 0.1421 0.1431 0.2885 0.3995 0.4746 0.5487 0 0.0368 0.1182 0.1183 0.1872 0.3122 0.3809 0.4690 0 0.0334 0.1643 0.3033

p

T

MPa

K

0.7354 0.7694 1.823 1.833 2.641 4.003 5.854 8.567 2.390 2.417 3.715 5.088 6.679 9.016 0.4084 1.851 1.861 3.352 4.860 6.784 8.714 0.6019 1.850 1.880 3.385 4.995 7.701 8.591 1.046 2.129 2.159 4.331 6.205 7.612 9.064 0.3361 0.8632 2.080 2.081 3.168 5.230 6.511 8.170 0.5725 1.072 3.137 5.488

313.2 313.1 313.15 313.1 313.15 313.2 313.2 313.1 313.1 313.15 313.1 313.3 313.2 333.1 333.15 333.1 333.1 333.1 333.15 353.1 353.1 353.1 353.1 353.15 373.05 373.05 373.05 373.05 373.05 373.05 373.05 373.05 393.05 393.05 393.05 393.05 393.1 393.05 393.05 413.1 413.0 413.0 413.05 413.0 413.1 413.05 413.05 433.05 433.0 433.05 433.0 433.05 433.05 433.05 433.05

m j KCl

m j CO2

mol‚kg-1 mol‚kg-1 4.05

4.05

4.05

3.998

3.998

3.998

3.998

0.0896 0.2082 0.2115 0.2241 0.2245 0.3651 0.3666 0.5130 0.6718 0.7838 0.8739 0.8867 0.8862 0.2118 0.3456 0.4644 0.5557 0.6228 0.7225 0.1614 0.2983 0.3975 0.4795 0.5878 0.0384 0.1150 0.1747 0.2879 0.4005 0.4056 0.4706 0.5070 0.0378 0.1104 0.1105 0.1852 0.3029 0.3767 0.4573 0 0.0372 0.1189 0.1953 0.1958 0.2719 0.3325 0.4073 0 0.0526 0.0538 0.1206 0.1866 0.2627 0.3412 0.3787

p MPa 0.5878 1.414 1.427 1.503 1.536 2.554 2.617 3.775 5.437 6.940 8.738 9.320 9.395 2.044 3.482 4.927 6.292 7.337 9.137 2.035 3.896 5.405 6.833 8.909 0.6092 1.720 2.633 4.508 6.653 6.755 8.156 9.031 0.7669 1.964 1.974 3.295 5.538 7.079 9.065 0.3078 0.9535 2.453 3.930 3.932 5.520 6.856 8.662 0.5248 1.509 1.529 2.835 4.209 5.846 7.653 8.597

(KCl + H2O), where the gas was volumetrically filled into the cell, the experimental uncertainty of the gas molality is estimated not to surmount 1 %. For the CO2 solubility measurements in (KOH + H2O), where the gas was gravimetrically filled into the cell, the estimated experimental uncertainty in the gas molality, resulting only from the gas filling procedure, ranges from about 0.25 % (at the highest gas solubilities) to a maximum of 0.9 % (at the lowest gas solubilities). In (CO2 + K2CO3 + H2O), the experimental uncertainty of the gas molality ranges from 0.4 % (at the highest gas solubilities) to a maximum of 2 % (at the lowest gas solubilities). Experimental Results. (a) System (CO2 + KCl + H2O). The solubility of carbon dioxide in aqueous solutions of potassium chloride was investigated at salt molalities m j KCl ≈ (2 and 4)

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Figure 2. Total pressure above aqueous solutions of (KCl + CO2) (a, m j KCl ≈ 2 mol‚kg-1; b, m j KCl ≈ 4 mol‚kg-1): b, T ≈ 313.5 K; O, T ≈ 333.1 K; 2, T ≈ 353.1 K, 4, T ≈ 373.1 K; 9, T ≈ 393.1 K; 0, T ≈ 413.1 K; ×, T ≈ 433 K) experimental results; s, correlation results.

mol‚(kg of water)-1 at temperatures T from about (313 to 433) K in about 20 K intervals and at pressures p up to about 9.4 MPa. The experimental results are given in Table 1. Figure 2 shows them plotted as the pressure against the gas molality m j CO2 at a preset temperature. As can be seen from Figure 2 and according to Henry’s law, initially the solubility pressure increases practically linearly with increasing gas molality at a given temperature. Furthermore, at a preset pressure and salt molality, the solubility of CO2 in (KCl + H2O) decreases with rising temperature. For example, at p ) 6 MPa, m j KCl ≈ 2 mol‚kg-1, and T ≈ (313, 353, and 413) K, the solubility of carbon dioxide amounts to m j CO2 ≈ (0.83, 0.5, and 0.36) mol‚kg-1, respectively. Figure 3 illustrates the “salting-out” effect induced by the presence of potassium chloride in the aqueous solution, meaning that at a preset temperature and pressure, the gas solubility is reduced by the presence of the salt. For example, at T ≈ 313.15 K, p ) 6 MPa, and m j KCl ≈ (0, 2, and 4) mol‚kg-1, the solubility of carbon dioxide amounts to m j CO2 ≈ (1, 0.83, and 0.7) mol‚kg-1, respectively. The broken curve in Figure 3 gives the correlation results for the solubility of carbon dioxide in pure water (at T ) 313.15 K) according to Rumpf and Maurer.15 Both the behavior of the purely physical gas solubility as well as the salting-out effect are in accordance with the results from previous investigations of the solubility of carbon dioxide in aqueous solutions of several strong electrolytes (for example, Na2SO4, NaCl, (NH4)2SO4, NH4Cl; see Rumpf et al.).15,24,25 (b) System (CO2 + K2CO3 + H2O). The solubility of carbon dioxide in aqueous solutions of potassium carbonate was investigated at stoichiometric molalities of the strong electrolyte m j K2CO3 ≈ (0.43 and 1.7) mol‚(kg of water)-1 (stoichiometric mass fraction of the salt w j K2CO3 ≈ 0.056 and 0.19, respectively), which correspond to stoichiometric molalities of potassium / ≈ (0.86 and 3.5) mol‚(kg of water)-1. The hydroxide of m j KOH temperatures were about (313, 353, and 393) K and the solubility pressure reached up to about 9.2 MPa. The experimental results are given in Table 2. Figures 4a and 5a show them plotted as the pressure required to dissolve the carbon dioxide against the gas loading m j CO2/m j K2CO3 at a preset temperature.

Figure 3. Total pressure above aqueous solutions of (KCl + CO2) at T ≈ 313.5 K: b, m j KCl ≈ 2 mol‚kg-1; O, m j KCl ≈ 4 mol‚kg-1, experimental results; s, correlation results; - - -, correlation results from Rumpf and Maurer15 for the solubility pressure above the aqueous salt-free solutions.

The vapor pressure behavior is the typical one observed when a sour gas is dissolved in an aqueous solution of a basic compound. When carbon dioxide is added to an aqueous solution of potassium carbonate, initially the total pressure above the solution (region II, 0 < m j CO2/m j K2CO3 < 1) only slightly deviates from the vapor pressure above the liquid mixture of (K2CO3 + H2O), because the volatile gas is almost completely chemically absorbed (see reaction II and Figure 1). However, when most potassium carbonate has reacted (region III, m j CO2/m j K2CO3 > 1), carbon dioxide becomes more and more physically dissolved, leading to a steep increase of the total pressure. Furthermore, at fixed pressure and stoichiometric molality of potassium carbonate, the solubility of CO2 in (K2CO3 + H2O) decreases

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From these two equations, the total pressure p and the vaporphase composition (yi is the vapor-phase mole fraction of component i) are calculated. kH,CO2(T) is Henry’s constant of carbon dioxide in pure water (based on the molality scale) at the vapor pressure of pure water {psW(T)}. Correlation equations for these two properties were adopted from Rumpf and Maurer15 and Saul and Wagner,26 respectively. The molar volume of liquid water, VW(T, p), was approximated by the molar volume of saturated liquid water, VsW(T), which was also taken from Saul and Wagner.26 The partial molar volume of carbon ∞ (T), was calculated as dioxide infinitely diluted in water, VCO 2 recommended by Brelvi and O’Connell27 (see also ref 28). R is the universal gas constant. The virial equation of state, which was truncated after the second virial coefficient, was used to calculate the vapor-phase fugacity coefficients of component i (φi) and of pure and saturated gaseous water (φsW). Pure component second virial coefficients BCO2,CO2 and BW,W were calculated from a correlation based on data recommended by Dymond and Smith.29 The mixed second virial coefficient BCO2,W was calculated as recommended by Hayden and O’Connell.30 Details on the calculation of all required second virial coefficients were given previously.28 Activities are calculated from Pitzer’s molality scale-based equation for the excess Gibbs energy (G E) of aqueous electrolyte solutions22, 23 (see Appendix 2). The activity of a solute species i follows from

Table 2. Experimental Results for the Total Pressure above Aqueous Solutions of Potassium Carbonate and Carbon Dioxide

a

T

m j K2CO3

m j CO2

p

K

mol‚kg-1

mol‚kg-1

MPa

313.2 313.25 313.2 313.2 313.2 313.2 313.2 353.1 353.1 353.1 354.15 353.1 353.1 353.1 353.1 393.15 393.2 393.2 393.2 393.2 393.15 393.2 393.2 313.75 313.75 313.85 313.85 313.9 313.75 353.05 353.0 353.05 353.05 353.05 353.0 393.0 393.05 393.05 393.05 393.0 393.0

0.4272a

0.4992 0.6252 0.6894 0.8272 0.9993 1.2549 1.5340 0.4637 0.5233 0.6471 0.6472 0.8926 0.9073 1.0394 1.1086 0.3650 0.4304 0.4714 0.5016 0.6076 0.7316 0.7795 1.0437 1.7371 2.0071 1.9861 2.1441 2.3362 2.5123 1.7233 1.8276 1.8391 1.9080 2.0240 2.1549 1.1683 1.5977 1.7174 1.7148 1.9024 2.0205

0.4299 1.029 1.450 2.224 3.373 5.362 8.980 0.490 0.9141 2.227 2.256 4.936 5.091 7.091 8.193 0.2702 0.4898 0.870 1.272 2.622 4.258 4.941 9.237 0.329 2.043 1.914 3.330 5.484 7.700 0.7683 1.667 1.831 2.564 4.642 6.672 0.2672 0.6854 1.317 1.463 4.174 6.376

0.4292b

0.4272a

1.7125c

1.7125c

1.7125c

ai )

mi ni ) / m° M n

Correlation of the Gas Solubility The reference state for the chemical potential of the solvent water is chosen to be the pure liquid at systems temperature and pressure, whereas for the chemical potential of a solute species (carbon dioxide and all ionic species present) it is the one molal solution of that solute in pure water at the temperature and pressure of the system, the solute experiencing the same interactions as if infinitely diluted in pure water. The VLE condition thereby results in the extended Henry’s law for carbon dioxide:

[

RT

]

aCO2 ) yCO2pφCO2

(1)

and in the extended Raoult’s law for water: psWφsW exp

[

]

VW(p - psW) aW ) yWpφW RT

(4)

W W

with rising temperature. For example, at p ) 6 MPa, m j K2CO3 ≈ 0.43 mol‚kg-1, and T ≈ (313, 353, and 393) K, the solubility of carbon dioxide amounts to m j CO2 ≈ (1.34, 0.97, and 0.85) mol‚kg-1, respectively.

∞ VCO (p - psW) 2

(3)

where mi is the (true) molality of solute species i (m° ) 1 mol‚ kg-1):

w j K2CO3 ) 0.05575. b w j K2CO3 ) 0.05599. c w j K2CO3 ) 0.19138.

kH,CO2 exp

mi γ m° i

(2)

where ni is the (true) number of moles of species i, M/W is the relative molar mass of water divided by 1000 (M/W ) 0.01801528), and nW is the (true) number of moles of water. The activity coefficient of a solute species γi (on the molality scale) is directly calculated from the G E equation, whereas the activity of the solvent water aW is calculated from the activity coefficients of all solute species by applying the Gibbs-Duhem equation. As already mentioned in previous work,31-34 when Pitzer’s E G equation is applied to chemical reacting systems, it is much easier to use the general equations for the activity coefficient of a solute species and for the activity of water as a function of (1) (2) the interaction parameters β(0) ij , βij , βij , and µijk, rather than using rearranged equations as a function of comprehensive (0) parameters (e.g., CφMX, BG,MX , ΓG,MX,MX, ΓG,G,MX, see Appendix 2). This does not increase the number of independent parameters but greatly simplifies the computer codes. Such a procedure was also applied in the present work. System (CO2 + KCl + H2O). Potassium chloridesas a strong electrolytesis assumed to completely dissociate in liquid water within the temperature and concentration ranges discussed here, that is, well below the solubility limit of the salt in water.12 Furthermore, when carbon dioxide is dissolved in an aqueous solution of potassium chloride (again within the temperature and concentration ranges discussed here), the dissociation of carbon dioxide in the liquid phase can be neglected.15,25

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Figure 4. Total pressure (a) and partial pressure of carbon dioxide (b) above aqueous solutions of (K2CO3 + CO2) {m j K2CO3 ≈ 0.428 mol‚kg-1 (w j K2CO3 ≈ 0.0557) }: b, T ≈ 313.2 K; O, T ≈ 353.1 K; 2, T ≈ 393.2 K, experimental results; s, prediction results. The “experimental result” for the partial pressure of carbon dioxide was calculated from the experimental result for the total pressure by subtracting the partial pressure of water, as predicted by the model.

Figure 5. Total pressure (a) and partial pressure of carbon dioxide (b) above aqueous solutions of (K2CO3 + CO2) {m j K2CO3 ) 1.7125 mol‚kg-1 (w j K2CO3 ) 0.19138)}: b, T ≈ 313.8 K; O, T ≈ 353 K; 2, T ≈ 393 K, experimental results; s, prediction results. The partial pressure of carbon dioxide was calculated from the experimental result for the total pressure by subtracting the partial pressure of water, as predicted by the model.

(a) Interaction Parameters in Pitzer’s G E Model. (i) System (CO2 + H2O). Following Rumpf and Maurer,15 the interaction (0) parameters βCO and µCO2,CO2,CO2 were set to zero. Rumpf 2,CO2 and Maurer’s correlation of the solubility of carbon dioxide in water covers a temperature range from about (273 to 413) K and is applicable for pressures well beyond 10 MPa. (ii) System (KCl + H2O). Parameters describing interactions between potassium and chloride ions in water (βK(0)+,Cl-, βK(1)+,Cl-, and CφKCl) were adopted from Holmes and Mesmer35 (see also Pitzer).36 They are valid for temperatures from about (273 to 523) K and up to the solubility limit of the salt,12 as long as the salt molality does not exceed 6 mol‚kg-1. According to the explanations given in Appendix 2, µK+,Cl-,Cl- was set to zero,

and µK+,K+,Cl- was calculated from 1 µK+,K+,Cl- ) CφKCl 3

(5)

To facilitate direct programing, the correlation equations for all Pitzer’s interaction parameters used in the present work (which are not equal to zero) are listed in Appendix 3. (iii) System (CO2 + KCl + H2O). Parameters describing interactions between carbon dioxide and potassium chloride in (0) , ΓCO2,KCl,KCl, and ΓCO2,CO2,KCl) were fit to the water (BCO 2,KCl new experimental results for the solubility of carbon dioxide in aqueous solutions of potassium chloride. Again following to

Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007 823

the explanations given in Appendix 2, in the computer codes, (0) + + the parameters βCO -, µCO2,K ,K , µCO2,Cl ,Cl , and µCO2,CO2,Cl 2,Cl were all set to zero arbitrarily. Then: (0) BCO 2,KCl

)

(0) βCO + 2,K

292.86 49047.9 ) 0.49547 + (T/K) (T/K)2

1 ) µCO2,K+,Cl- ) -0.000989 Γ 2 CO2,KCl,KCl ΓCO2,CO2,KCl ) µCO2,CO2,K+ ) -0.039588 +

12.008 (T/K)

(6)

(7) (8)

Figure 2 illustrates the very satisfactory agreement between the experimental results (symbols) and the correlation results (curves) for the total pressure above liquid mixtures of (CO2 + KCl + H2O). The absolute and relative average deviations between the experimental and calculated results amount to ( 0.06 MPa and ( 1.3 %, respectively. System (CO2 + K2CO3 + H2O). As already mentioned, when carbon dioxide is dissolved in an aqueous solution of potassium carbonate, three reversible chemical reactions occur: the autoprotolysis of water H2O(l) h H+(aq) + OH-(aq)

(III)

and the formation of bicarbonate (HCO3-) and carbonate (CO32-) -

+

CO2(aq) + H2O(l) h HCO3 (aq) + H (aq)

(IV)

HCO3-(aq) h CO32-(aq) + H+(aq)

(V)

The condition for chemical equilibrium for a chemical reaction r () III, IV, and V) is Kr(T) )

∏a

νi,r i

(9)

i

Chemical reaction equilibrium constants (on the molality scale) were adopted from the literature (KIII from Edwards et al.,19 KIV from Patterson et al.,20 and KV from Patterson et al.,21 see also ref 37). The influence of pressure on Kr is neglected. νi,r is the stoichiometric factor of reactant i in reaction r (νi,r > 0 for a product and νi,r < 0 for an educt). The balance equation for the amount of substance (the number of moles) of a species i in the liquid solution is ni ) n˜ i +

∑ν

i,r

ξr

(10)

r

where ξr is the extent of reaction r. Solving this set of equations for a given temperature and stoichiometric amounts (moles) of substances n˜ i of H2O, K+, CO32-, and CO2 gives the “true” composition of the liquid phase (i.e., the amount of substance ni of all species present). In addition, in such solutions, the salt potassium bicarbonate may precipitate from the liquid mixture (see, e.g., Benson et al.):1 KHCO3(s) h K+(aq) + HCO3-(aq)

(VI)

In the absorption/desorption processes (with or without any activating additives), the deposition of potassium bicarbonate has to be avoided. Hence, it is important to know about the range of conditions where the salt precipitates. Therefore, the

model was extended to allow for a deposition of the salt. The phase equilibrium condition yields: Ksp,KHCO3(T) ) aK+aHCO3-

(11)

Ksp,KHCO3 is the solubility product for the formation of solid potassium bicarbonate (on the molality scale). The influence of pressure on Ksp,KHCO3 is neglected. If the activity product (right-hand side of eq 11) is below the solubility product, potassium bicarbonate will not precipitate from the liquid mixture. Some salt will precipitate only if the solubility product is reached. Ksp,KHCO3(T) was determined in the present work. Details are given below. (a) Additional Interaction Parameters in Pitzer’s G E Model. (i) System (KOH + H2O). Because the amount of hydroxide ions dissolved in liquid mixtures of (CO2 + K2CO3 + H2O) is always very small in comparison with the amount of other solute species, parameters describing interactions between potassium and hydroxide ions in water have only a relatively small influence here, even though, they were included in the program φ files. βK(0)+,OH-, βK(1)+,OH-, and CKOH were adopted from Pitzer and 38 23, Mayorga (see also Pitzer). 36 These parameters are strictly only valid at temperatures around 298 K and for potassium hydroxide molalities up to 5.5 mol‚kg-1. Again according to the explanations given in Appendix 2, µK+,OH-,OH- was set to zero, and µK+,K+,OH- was calculated from 1 φ µK+,K+,OH- ) CKOH 3

(12)

(ii) System (K2CO3 + H2O). First, it is important to know about the solubility of potassium carbonate in water (see Linke and Seidell12 and Moore et al.39). Large amounts of potassium carbonate can be dissolved in water. For example, at T ) (298, 323, 348, 373, 398, 423, 448, 473, 498, and 523) K, the molality of K2CO3 at saturation in water amounts to about (8.1, 8.8, 9.8, 11.3, 13.6, 16.7, 17.4, 18.1, 18.9, and 19.2) mol‚kg-1, respectively. The literature indicates that for 298 K < T < 429 K the stable solid phase is K2CO3‚1.5H2O.12,39 Above 429 K, a change in the crystal structure was experimentally observed,39 but the solid phase at this elevated temperature has not been identified yet. Because of the high solubility of potassium carbonate in water, well beyond the salt concentrations that are of interest in connection with the Hot Potassium Carbonate Process and its modifications, it was not necessary to extend the model to account for the deposition of K2CO3‚1.5H2O, etc. When potassium carbonate is dissolved in pure water, with the exception of very dilute solutions, chemical reactions can be neglected (see Figure 1). Thus, Pitzer’s parameters describing interactions between potassium and carbonate ions in water (βK(0)+,CO32-, βK(1)+,CO32-, and CKφ 2CO3) may be straightforwardly determined from experimental results for the VLE of that system. Aseyev’s11 compilation of experimental data for the total pressure above aqueous solutions of potassium carbonate covers wide ranges both in temperature (T ) 298 K to 623 K) and in composition {up to w j K2CO3 ) 0.5 (m j K2CO3 ≈ 7.2 mol‚kg-1) for j K2CO3 ≈ 10.9 mol‚kg-1) T up to 393 K, up to w j K2CO3 ) 0.6 (m for T from (398 to 518) K, up to w j K2CO3 ) 0.7 (m j K2CO3 ≈ 16.9 mol‚kg-1) for T from (523 to 568) K, and up to w j K2CO3 ) 0.76 (m j K2CO3 ≈ 22.9 mol‚kg-1) for higher temperatures}. Some selected data from Aseyev’s compilation {at T ) (298, 323, 348, 363, 383, and 398) K, and for stoichiometric mass fractions of the salt up to w j K2CO3 ) 0.5} were used to determine the aforementioned parameters. Again according to the explanations given in Appendix 2, µK+,CO32-,CO32- was set to zero, and

824

Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007

{measured at temperatures from about 298 K to 363 K and at w j K2CO3 up to about 0.51 (m j K2CO3 ≈ 7.5 mol‚kg-1)} are shown in Figure 6 for comparison. They agree perfectly with Aseyev’s data and with the calculated results from the new model (relative average deviation between experimental and calculated results for the pressure ≈ ( 0.7%). Apelblat41 reported vapor pressures of water over aqueous solutions of potassium carbonate at temperatures from (283 to 313) K, however, only at saturation (i.e., at high salt concentrations beyond the range of interest). Therefore, these data were not taken into account to determine the pertaining Pitzer parameters. It may also be interesting to compare the results for the osmotic coefficient of liquid mixtures of (K2CO3 + H2O), resulting from the experimental data for the total pressure by Aseyev11 and by Puchkov and Kurochkina,40 with calculation results from the model. Neglecting all chemical reactions to determine the activity of water in the ideal solution, the molality scale-based osmotic coefficient in the system is φ)-

ln aW m j K2CO3 3M/W m°

(17)

The activity of water is calculated from the extended Raoult’s law by again calculating the fugacity coefficient of pure water in the gaseous phase from the truncated virial equation of state: Figure 6. Total pressure above aqueous solutions of K2CO3 at T ) (298.15 to 473.15) K: b, experimental data as compiled by Aseyev;11 O, experimental data from Puchkov and Kurochkina;40 4, calculated from isopiestic data by Sarbar et al.42 (see text); s, correlation/prediction, this work (see text).

x2 φ C 6 K2CO3

(13)

The resulting parameters are 82.857 (T/K)

(14)

6974.6 (T/K)

(15)

βK(0)+,CO32- ) 0.38621 βK(1)+,CO32- ) 21.975 -

µK+,K+,CO32- ) -0.00872 +

2.69 (T/K)

(16)

As can be seen from Figure 6, the correlation gives a very good description of Aseyev’s vapor pressure data (at least up to w j K2CO3 ) 0.5) for temperatures ranging from 298 K to at least 473 K. In these regions, the relative average deviation between the experimental and calculated results amounts to about ( 1 %. As expected, beyond w j K2CO3 ) 0.5, the deviation between the experimental and calculated results for the total pressure increases with rising mass fraction of the salt and with rising temperature. However, the concentration and temperature ranges with relatively large deviations between experimental and calculated results are not of interest in connection with the Hot Potassium Carbonate Process and its modifications; therefore, no attempt was made to improve the correlation there. The experimental data for the total pressure above liquid mixtures of (K2CO3 + H2O) from Puchkov and Kurochkina40

[

]

∆p ∆p + ln 1 - s RT p W

(18)

where ∆p is the vapor pressure depression arising from the addition of potassium carbonate to pure liquid water: ∆p ) psW - p

µK+,K+,CO32- was calculated from µK+,K+,CO32- )

ln aW ) (VW - BW,W)

(19)

As expected, but not at all temperatures, the osmotic coefficient data resulting from the total pressure from Aseyev11 and from Puchkov and Kurochkina40 agree reasonably with the calculated results from the model (see Figure 7). Furthermore, Sarbar et al.42 carried out isopiestic investigations of liquid mixtures of (K2CO3 + H2O) at T ) 298.15 K and at m j K2CO3 ) (0.13 to 8.1) mol‚kg-1. As can be seen from Figure 7, the osmotic coefficients resulting from the isopiestic data of Sarbar et al.42 systematically deviate (in average by about +0.12) from the new correlation. That is, they deviate from the osmotic coefficients resulting from the vapor pressure data by Aseyev.11 Consequently, the vapor pressure data resulting from the isopiestic data of Sarbar et al.42 also systematically deviate from the new correlation, by about -0.1 % at the lowest stoichiometric salt molality up to about -5.8 % at one of the highest stoichiometric salt molalities (see Figure 6). The data by Sarbar et al.42 were therefore excluded from the fitting procedure. (iii) Systems (KHCO3 + H2O) and (K2CO3 + KHCO3 + H2O). As explained in Appendix 1, an aqueous solution of potassium bicarbonate is equivalent to an aqueous (stoichiometrically) equimolar solution of carbon dioxide and potassium carbonate. As can be seen from Figure 1, in such a solution chemical reactions III to V cannot be neglected, and the solution contains appreciable amounts of carbon dioxide in molecular form. Hence, Pitzer’s parameters involving the species carbon dioxide may play an essential role here. It is therefore not recommended to determine the relevant Pitzer’s parameters for interactions between potassium and bicarbonate in water from

Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007 825

Figure 7. Molality scale-based osmotic coefficient of aqueous solutions j K2CO3/m°)} at constant temof potassium carbonate φ ) ln aW/{-3M/W(m perature: a, T ) 298.15 K; b, T ) 323.15 K; c, T ) 348.15 K; d, T ) 363.15 K; e, T ) 383.15 K; f, T ) 398.15 K. b, O evaluated from experimental data for the total pressure above (K2CO3 + H2O) as compiled by Aseyev11 and from Puchkov and Kurochkina,40 respectively (see text). 4, calculated from isopiestic data by Sarbar et al.42 (see text); s, correlation/ prediction, this work (see text).

VLE data for the system (KHCO3 + H2O). However, in aqueous solutions of carbon dioxide and potassium carbonate, and at gas loadings m j CO2/m j K2CO3 well below 1, carbon dioxide is almost completely converted to bicarbonate. Here, following Appendix 2, only parameters describing interactions between potassium and carbonate (βK(0)+,CO32-, βK(1)+,CO32-, and CKφ 2CO3), which were already determined as described above, as well as between φ ), potassium and bicarbonate (βK(0)+,HCO3-, βK(1)+,HCO3-, and CKHCO 3 and in principle also between potassium, carbonate, and bicarbonate (µK+,CO32-,HCO3-) are important. Three attempts were made to determine the missing parameters. In a first attempt, µK+,CO32-,HCO3- was set to zero, and only φ (βK(0)+,HCO3-, βK(1)+,HCO3-, and CKHCO ) were fit to the data base for 3 the partial pressure of carbon dioxide (pCO2) above liquid mixtures of (CO2 + K2CO3 + H2O) by Tosh et al.3 In that investigation, T ≈ (343 to 413) K, w j K2CO3 ) 0.2, 0.3, and 0.4 {m j K2CO3 ≈ (1.8, 3.1, and 4.8) mol‚kg-1}, m j CO2/m j K2CO3 ≈ 0.1 to 0.87, and pCO2 amounts up to about 0.92 MPa. The influence of temperature on these parameters was described by means of the common equation, f(T) ) a + b/(T/K). The model

satisfactorily represented the data. The average relative deviation between the experimental and the correlation results for pCO2 amounted to ( 11.1 % over the entire range of conditions (( 8.7 %, ( 9 %, and ( 13.3 % at w j K2CO3 ) 0.2, 0.3, and 0.4, respectively). It might be noted, that no appreciable improvement was achieved by taking additionally into account the parameter µK+,CO32-,HCO3- in the correlation (cf., Chen et al.43). Next, some literature data for the solubility of potassium bicarbonate in aqueous solutions of the stoichiometric components carbon dioxide and potassium carbonate (all data are, however, within region II) were considered: the data compiled included that of Seidell and Linke12 {for systems KHCO3 + H2O (273 K < T < 343 K) and K2CO3 + KHCO3 + H2O (278 K < T < 323 K)}, Hill and Hill13 {for system K2CO3 + KHCO3 + H2O (298 K < T < 309 K)}, and Benson et al.1 {for system K2CO3 + KHCO3 + H2O (301.9 K < T < 415.4 K)}. The solubility data reported by Lyudkovskaya et al.,44 for the system K2CO3 + KHCO3 + H2O (301.9 K < T < 415.4 K), are not in accordance with the data of Benson et al.1 and were therefore discarded. By applying the model with the new parameters, the solubility product of potassium bicarbonate Ksp,KHCO3 was calculated from the saturation data1,12,13 at the different temperatures. However, a large scattering was observed in the calculated values, and it was not possible to correlate the results by only considering the influence of temperature on Ksp,KHCO3. In a second attempt, µK+,CO32-,HCO3- again was set to zero, φ ) as well as Ksp,KHCO3 were and (βK(0)+,HCO3-, βK(1)+,HCO3-, CKHCO 3 simultaneously adjusted to both the VLE data (pCO2) by Tosh et al.3 and the SLE data by Benson et al.,1 Seidell and Linke,12 and Hill and Hill.13 The influence of temperature on all these parameters (including ln Ksp,KHCO3) was again described by f(T) ) a + b/(T/K). However, this procedure resulted in a much worse description of the VLE data and in a barely appreciable improvement in the representation of the SLE data. Last, in a third and successful attempt, µK+,CO32-,HCO3was taken into account as well: µK+,CO32-,HCO3-, (βK(0)+,HCO3-, φ βK(1)+,HCO3-, CKHCO ), and Ksp,KHCO3 were simultaneously adjusted 3 to both the VLE and the SLE data mentioned before. The influence of temperature on all these parameters (including ln Ksp,KHCO3) was again described by f(T) ) a + b/(T/K). In addition, according to the explanations given in Appendix 2, in the program codes µK+,HCO3-,HCO3- was set to zero, and µK+,K+,HCO3- was calculated from 1 φ µK+,K+,HCO3- ) CKHCO 3 3

(20)

The resulting parameters are

βK(0)+,HCO3- ) 0.10662 βK(1)+,HCO3- ) 8.19 -

40.439 (T/K)

2648 (T/K)

µK+,K+,HCO3- ) -0.000348 +

ln Ksp,KHCO3 ) 16.1646 -

(22)

0.215 (T/K)

µK+,CO32-,HCO3- ) -0.0000118 -

(21)

0.2181 (T/K)

4974.48 (T/K)

(23) (24) (25)

The model then resulted in a very reasonable description of both the VLE data3 and the SLE data.1,12,13 The average relative

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Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007

Figure 8. Partial pressures of carbon dioxide (a) and water (b) above aqueous solutions of carbon dioxide and potassium carbonate at preset temperature and gas-free liquid-phase composition {(A) w j K2CO3 ) 0.2 (m j K2CO3 ≈ 1.809 mol‚kg-1); (B) w j K2CO3 ) 0.3 (m j K2CO3 ≈ 3.101 mol‚kg-1); (C) w j K2CO3 ) 0.4 (m j K2CO3 ≈ 4.824 mol‚kg-1)}. Symbols ) experimental data from Tosh et al.3 (b, T ) 343.15 K; O, T ) 363.15 K; 2, T ) 383.15 K; ×, T ) 393.15 K; 4, T ) 403.15 K; /, T ) 413.15 K). s, correlation for pCO2; prediction for pW, this work.

deviation between the experimental results for the partial pressure of carbon dioxide from Tosh et al.3 and the calculated results amounts to ( 12.2 % over the entire range of conditions (( 10 %, ( 9.2 %, and ( 14.7 % at w j K2CO3 ) 0.2, 0.3, and 0.4, respectively). In Figure 8, the experimental data for the partial pressure of carbon dioxide pCO2 (and water pW) from Tosh et al.3 are plotted against the gas loading m j CO2/m j K2CO3 at preset temperature and gas-free liquid-phase composition w j K2CO3 ) 0.2, 0.3, and 0.4 {m j K2CO3 ≈ (1.8, 3.1, and 4.8) mol‚kg-1}, respectively. The curves in the figure represent the correlation results for pCO2 and the prediction results for pW. Within the whole range of conditions investigated by Tosh et al.,3 and in accordance with the experiment, no precipitation of potassium bicarbonate is predicted by the model. The vertical bars in Figure 8C denote the predictions of the model for the limit, at which addition of more carbon dioxide to the aqueous solution of carbon dioxide and potassium carbonate with w j K2CO3 ) 0.4 result in a deposition of potassium bicarbonate. In Figure 9, the solubility product of potassium bicarbonate in water is plotted against the temperature. The solid line represents the present correlation (eq 25). Symbols denote the numerical values for ln (aK+aHCO3-) of the saturated liquid mixture calculated from Pitzer’s model (with the given interaction parameters) at temperatures and compositions reported in refs 1, 12, and 13. To allow for a quantitative comparison between the experimental and calculated results at saturation, the potassium bicarbonate saturation temperature was calculated from the present model at a preset liquid-phase composition and compared with the aforementioned data1,12,13 (see Figure 10). Over the entire range of conditions, the average absolute deviation between the experimental and calculated temperatures amounts to about ( 3 K. It might be noted, that Roy et al.45 reported a set of Pitzer parameters (βK(0)+,CO32-, βK(1)+,CO32-, CKφ 2CO3), (βK(0)+,HCO3-, φ (0) (0) 2+ ), βCO βK(1)+,HCO3-, CKHCO 2-, µK ,CO3 ,HCO3 (and βCO 2-,Cl-, 3 3 ,HCO3 3 µK+,CO32-,Cl-, µK+,HCO3-,Cl-), which might have been adopted here 45 (the correlation by Roy et al. does not include unsymmetrical mixing terms in Pitzer’s equation). That set was adjusted by those authors to the isopiestic data for the system (K2CO3 + H2O) given by Sarbar et al.,42 to their earlier electromotive force

Figure 9. Solubility product of potassium bicarbonate in water (ln Ksp,KHCO3) plotted against the temperature. The solid line denotes correlation results for ln Ksp,KHCO3 according to eq 25, this work (see text). Symbols denote results from the model presented here for ln (aK+aHCO3-) calculated from saturation data from different sources: b, compilation by Seidell and Linke12 (system KHCO3 + H2O); O, compilation by Seidell and Linke12 (system K2CO3 + KHCO3 + H2O); ], Hill and Hill13 (system K2CO3 + KHCO3 + H2O); 9, Benson et al.1 (system K2CO3 + KHCO3 + H2O).

(emf) data in aqueous mixtures of KHCO3, KCl, and CO2,46 and to their emf data in aqueous mixtures of K2CO3, KHCO3, and KCl.45 These investigations cover a temperature range from (278 to 318) K. Applying that parameter set leads to considerably larger deviations between experimental results and calculated (i.e., predicted) results for both the total pressure above liquid mixtures of (K2CO3 + H2O)11,40 and for the partial pressure of carbon dioxide above liquid mixtures of (CO2 + K2CO3 + H2O) in the low gas loading region4 than the correlation presented here. Some other sets of parameters for those systems were provided by Roy et al.45 and by Simonson et al.47 In particular, Simonson et al.47 extended the temperature range up to 368 K by considering some additional emf data in aqueous mixtures of KHCO3, KCl, and CO2. These parameter sets could not be tested here, because in these correlations unsymmetrical mixing terms were included in Pitzer’s equation. Because the liquid mixtures investigated by Roy et al.45,46 and

Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007 827

Figure 10. (Tcalc - Texp) plotted against Texp, where T is the potassium bicarbonate saturation temperature at preset liquid-phase composition. (Subscripts exp and calc denote experimental data and calculation results from the present model, respectively.) b, compilation by Seidell and Linke12 (system KHCO3 + H2O); O, compilation by Seidell and Linke12 (system K2CO3 + KHCO3 + H2O); ], Hill and Hill13 (system K2CO3 + KHCO3 + H2O); 9, Benson et al.1 (system K2CO3 + KHCO3 + H2O).

by Simonson et al.47 contained considerable amounts of potassium chloride, these emf data were not included in the fitting runs in the present work. (iW) Systems (CO2 + K2CO3 + H2O) and (CO2 + KHCO3 + H2O). In the thermodynamic model used to describe the solubility of carbon dioxide in aqueous solutions of potassium carbonate, Pitzer’s parameters for interactions between carbon (0) dioxide and potassium carbonate (BCO , ΓCO2,K2CO3,K2CO3, 2,K2CO3 and ΓCO2,CO2,K2CO3) as well as between carbon dioxide and (0) potassium bicarbonate (BCO , ΓCO2,KHCO3,KHCO3, and 2,KHCO3 ΓCO2,CO2,KHCO3) are still lacking. As can be seen from Figure 1, at very high gas loadings well beyond m j CO2/m j K2CO3 ) 1, only the species potassium, bicarbonate, and carbon dioxide appear in appreciable amounts, whereas at gas loadings around 1, carbonate appears in a smaller amount as well. Therefore, to determine the mentioned parameters one may use gas solubility data in those areas. However, in particular within the temperature and gas-free liquid-phase composition ranges which are of importance in connection with the Hot Potassium Carbonate Process (343 K < T < 413 K, 0.2 < w j K2CO3 < 0.4, i.e., 1.8 mol‚kg-1 < m j K2CO3 < 4.8 mol‚kg-1), no such experimental information was found in the open literature. Therefore, a more or less pragmatic approach is accomplished here: Pitzer’s parameters for interactions between carbon di(0) + + + oxide and potassium ions (βCO +, µCO2,CO2,K , and µCO2,K ,K ), 2,K which had already been fixed previously (the first two according to eqs 6 and 8, the latter was set to zero), are adopted here. As described previously, these parameters are based on the solubility pressures above liquid mixtures of (CO2 + KCl + H2O) from the present work and are thereby valid for temperatures from (313 to 433) K, so they cover the relevant temperature range for the Hot Potassium Carbonate Process. All other (0) (0) 2+ missing parameters (that is, βCO 2-, βCO ,HCO -, µCO2,K ,CO3 , 2,CO3 2 3 22+ µCO2,CO3 ,CO3 , µCO2,K ,HCO3 , µCO2,HCO3 ,HCO3-, µCO2,CO2,CO32-, and µCO2,CO2,HCO3-) are set to zero. This results in (cf. Appendix 2):

and

(0) (0) BCO ) 2βCO + 2,K2CO3 2,K

(26)

ΓCO2,K2CO3,K2CO3 ) 0

(27)

ΓCO2,CO2,K2CO3 ) 2µCO2,CO2,K+

(28)

(0) (0) ) βCO BCO + 2,KHCO3 2,K

(29)

ΓCO2,KHCO3,KHCO3 ) 0

(30)

ΓCO2,CO2,KHCO3 ) µCO2,CO2,K+

(31)

(0) + Thus, by simply including βCO + and µCO2,CO2,K (according to 2,K eqs 6 and 8) for calculating the VLE of the system (CO2 + K2CO3 + H2O), the model allows for predictions of the carbon dioxide solubility pressure in the higher gas loading ranges. Calculated results may be checked by comparison with the few experimental results for the gas solubility reported in the present work. As can be seen from Figures 4a and 5a, the quality of these predictions is remarkable. The average absolute deviation between the experimental results for the total pressure and the prediction results amounts to ( 0.16 MPa over the entire range of conditions (( 0.12 MPa and ( 0.21 MPa at w j K2CO3 ≈ 0.056 (0) + are set to and 0.19, respectively). If βCO + and µCO2,CO2,K ,K 2 zero, those deviations amount to ( 0.67 MPa (( 0.46 MPa and ( 0.93 MPa, respectively). Figures 4b and 5b also illustrate the good agreement between the partial pressure of carbon dioxide as calculated from the experimental total pressures by subtracting the partial pressure of water (as predicted by the model) and the calculated results from the model.

Comparison with Literature Data System (CO2 + KCl + H2O). Table 3 reports average relative and absolute deviations between experimental results for the total pressure and the partial pressure of carbon dioxide above liquid mixtures of (CO2 + KCl + H2O) taken from the literature as well as from the present work and correlation/prediction results from the present model. The experimental ranges for the temperature, the stoichiometric molalities of potassium chloride and carbon dioxide, and the total pressure or the partial pressure of carbon dioxide of all the investigations are also given in Table 3. The data by Markham and Kobe48 (which were taken solely at pCO2 ) 1 atm) and by Yasunishi and Yoshida49 (which were taken only at p ) 1 atm) agree very well with calculated results from the new model (that is, they agree with the new experimental results). However, the data by Kiepe et al.,50 which were taken at pressures up to 10.5 MPa, widely differ from the results calculated by the model {in average by 0.53 MPa [12.1 %]}. That indicates that the data by Kiepe et al.50 severely disagree with the new experimental results. In Figure 11, both the experimental data (symbols) for the total pressure above aqueous solutions of potassium chloride as reported by Kiepe et al.50 and the prediction results from the new model (solid curves) are plotted against the molality of carbon dioxide in the liquid (at a preset temperature and at several salt molalities) for comparison. Kiepe et al.50 also report some experimental results for the solubility pressure above the salt-free system (CO2 + H2O), which are plotted in Figure 11 as well (only at two temperatures), and which again severely disagree {in average by 0.75 MPa (13.7 %)} with the correlation results from the model by Rumpf and Maurer15 (broken curves). This model was based on an extensive experimental database from the literature for the solubility of carbon dioxide in water and has been confirmed in a long series of experimental investigations in aqueous solutions of strong and weak electrolytes and in aqueous solutions of organic compounds (see, e.g., refs 15, 16, 24, 25, 28, 33, and 34). System (CO2 + K2CO3 + H2O). Table 4 lists the average relative and absolute deviations between experimental results

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Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007

Table 3. Comparison between Experimental Data from the Literature for the Total Pressure and the Partial Pressure of CO2 above Liquid Mixtures of (CO2 + KCl + H2O) and Calculation Results from the Present Model experimental ranges

average deviations

T

m j KCl

m j CO2

p

pCO2

|∆p/p|

|∆p|

|∆pCO2/pCO2|

|∆pCO2|

Na

K

mol‚kg-1

mol‚kg-1

MPa

MPa

%

MPa

%

MPa

Correlation this work

98

313-433